Jack and Jill have just had their first child.  If college is expected to cost ​$150 comma 000 per year in 18 ​years, how much should the couple begin depositing annually at the end of the next 18 years to accumulate enough funds to pay 1 year of tuition 18 years frm​ now?  Assume that they can earn a 6​% annual rate of return on their investment.
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Part 1
The amount that the couple should begin depositing annually at the end of each year is ​$
  
enter your response here.  ​(Round to the nearest​ cent.)

We can solve this problem using the future value of an annuity formula, because Jack and Jill need to know how much to deposit each year to reach a specific amount in 18 years. Here's how we break it down:

1. **Future Value Needed**:  
   Jack and Jill need to accumulate enough for **1 year of tuition** 18 years from now, which is $ \$150,000 $.

2. **Annual Interest Rate**:  
   The couple is expected to earn a 6% return on their investment annually.

3. **Number of Years**:  
   They have 18 years to accumulate the funds.

### The Future Value of an Annuity Formula:
\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:  
- $FV$ is the future value (the amount they need in the future, \$150,000).  
- $P$ is the annual payment (this is what we're solving for).  
- $r$ is the annual interest rate (6% or 0.06).  
- $n$ is the number of years (18 years).

Rearrange the formula to solve for $P$:
\[
P = \frac{FV \times r}{(1 + r)^n - 1}
\]

Now, substitute the values:
- $FV = 150,000$
- $r = 0.06$
- $n = 18$

\[
P = \frac{150,000 \times 0.06}{(1 + 0.06)^{18} - 1}
\]

Let's calculate this next.The couple should begin depositing approximately **$4,853.48** annually at the end of each year to accumulate enough funds for one year of college tuition 18 years from now, assuming a 6% annual rate of return.

Would you like further details or have any other questions?

Here are 5 related questions for further exploration:
1. How much would they need to deposit annually if tuition were expected to be $200,000 per year?
2. How does changing the interest rate to 5% affect the annual deposit required?
3. What if they want to save for 4 years of tuition instead of just 1 year?
4. How much would they need to deposit monthly instead of annually?
5. What if they started saving 10 years before college instead of 18?

**Tip:** When investing, compound interest plays a significant role over time, so starting early can reduce the required annual deposit.

Jack and Jill have just had their first child. If college is expected to cost $150,000 per year in 18 years, how much should the couple begin depositing annually at the end of the next 18 years to accumulate enough funds to pay 1 year of tuition 18 years from now? Assume that they can earn a 6% annual rate of return on their investment.

Discover how to calculate how much Jack and Jill need to deposit annually to save $150,000 for college tuition in 18 years, using the Future Value of Annuity formula and assuming a 6% annual interest rate. This problem involves compound interest and algebra, suitable for Grades 10-12.

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